Applications in computational vision such as ego-motion estimation and tracking often require imaging a large field of view. It is also desirable for an imaging system to have a single viewpoint in order to produce geometrically correct perspective images from the panoramic images obtained from the imaging system. The single and fixed viewpoint constraint requires that an imaging system only capture light that is passing through a single point in three dimensional space, thus sampling the 5-dimensional plenoptic function at that point, which is known as the effective viewpoint. Such imaging systems have been realized by assemblies of curved mirrors and lenses. Although these catadioptric systems can have a large field of view and can satisfy the single viewpoint requirement they are cumbersome, expensive and large.
A number of wide field of view optics use facing mirrors to produce high quality images at the expense of an obscuration of the field of view. A simple example of a prior art optical system 10 of such type is shown in FIG. 1. System 10 has two facing mirrors 12, 14 aligned on an optical axis 16. Mirror 14 receives and reflects light from a scene 20 to mirror 12. Mirror 12 reflects the light back to mirror 14 such that the light passes a central aperture 18 in mirror 14 and projects an image 22 of scene 20 on a screen 24.
Mirror 12 obscures a cone-shaped central portion 26 of the field of view seen by mirror 14. The result of this obscuration is a shadow 28 in image 22. To be imaged, light arriving from scene 20 has to be incident on mirror 14 at an angle larger than the angle of cone 26, e.g., at an angle of incidence θi relative to axis 16.
The prior art contains teachings about telescopes and other systems that employ the above-described principles. For example, U.S. Pat. No. 5,089,910 to Sigler teaches a catadioptric zoom relay telescope with two mirrors of which the first mirror or primary mirror is aspheric. U.S. Pat. No. 5,940,222 to Sinclair et al. teaches catadioptric zoom lens assemblies employing these same principles.
Some applications such as robot vision and panoramic imaging require the optical system to have a single point of view or viewpoint. This condition enables the optical system to produce a perspective view of objects in its field of view. In some applications, it is further desirable to maximize the size of the field of view imaged from the single viewpoint.
It is difficult to satisfy all of the above conditions with a single system. The catadioptric zoom relay telescopes and lens assemblies are usually limited to a small field of view and many do not have a single viewpoint. In fact, many high quality systems offer excellent on-axis performance, e.g., as taught by Hicks in U.S. Pat. No. 6,412,961 but are inherently not single viewpoint. U.S. Pat. No. 5,473,474 to Powell teaches a panoramic lens that images a large field of view but lacks a single viewpoint. Still another approach using the facing mirrors configuration is taught by Kuroda et al. in U.S. Pat. No. 5,854,713. This patent describes a reflection type angle of view transforming optical apparatus that is hollow but also lacks a single viewpoint. Of further interest is the catadioptric system of Charles shown in U.S. Pat. No. 6,449,103. Additional references of interest include U.S. Pat. No. 4,566,763 teaching the use of a parabolic reflector and U.S. Application No. 2003/0142203 teaching the use of a hyperbolic reflector.
The prior art does teach some systems that have a single viewpoint. For example, U.S. Pat. No. 3,505,465 to Rees discloses how to use a hyperbolic mirror to produce a single viewpoint system for a person viewing an image such as a TV or video image produced, e.g., by a video camera. More recently, U.S. Pat. Nos. 5,760,826 and 6,118,474 to Nayar describe an imaging apparatus for imaging a scene with a substantially paraboloid-shaped reflector whose focus is coincident with the single viewpoint. The imaging apparatus has a telecentric means optically coupled to the paraboloid-shaped reflector for filtering out principal rays of electromagnetic radiation that are not orthographically reflected by the paraboloid-shaped reflector.
Unfortunately, none of the prior art teachings provide a compact, effective and easy to manufacture single viewpoint lens that can be used in vision systems requiring a panoramic projection or perspective view of objects distributed over a large field of view.